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Simposio de Metrología 2016
19 al 23 de Septiembre de 2016
DESIGN OF A DIGITALLY ASSISTED BRIDGE FOR COMPARING FOURTERMINAL IMPEDANCES
A. H. Pacheco Estrada, J. A. Moreno Hernández, and F. L. Hernández Márquez
Centro Nacional de Metrología
km 4.5 Carretera a Los Cués, Municipio El Marqués, Qro. C.P. 76246 México
Tel. +52 442 211 05 00 (3361), [email protected]
Abstract: With the goal of establish the ohm-farad traceability chain at CENAM, it is being developed a
Digitally Assisted Bridge for Comparing Four-Terminal Impedances. This paper exposes the main parts of the
bridge and presents the model which describes the on balance bridge impedances ratio. The advantages
against Classic Impedance Bridges are discussed.
1.
INTRODUCTION
signals to balance the bridge instead of networks of
passive electromagnetic devices. The PSS is
controlled by a PC program which can adjust the
phase and amplitude of the signals, which varies the
in-phase and quadrature components of the bridge
balance signals automatically. The PSS also provide
the reference signal of the Bridge.
The Digitally Assisted Impedance Bridge (DAIB)
under development at CENAM is a measurement
system that compares two impedance standards at
1:1 and 10:1 ratios. This kind of bridge combines the
accuracy of an Inductive Voltage Divider (IVD),
which provides the reference ratio of the bridge [1],
and the versatility of the Programmable Sinewave
Synthesizer (PSS) to provide balance signals to the
bridge [2].
Figure 1 shows a simplified diagram of the Bridge,
which consists of five voltage signals from the PSS
(Va, Vb, Vc, Vd and Vw), injection transformers (Tb, Tc,
Td and Tw), impedances to be compared (Rx and Rs),
detection transformers (T2, T3 and T4), a null detector
to measure four balance nodes (n1, n2, n3 and n4), a
power supply transformer Tp, a Kelvin Inductive
Divider Tk and an IVD (TI). Furthermore, coaxial
chokes are distributed on each loop of the bridge to
suppress magnetic coupling and ground loops.
For many years, Classic Impedance Bridges have
been designed using complex networks of passive
electromagnetic devices (IVD, resistance decades,
capacitance boxes, etc.), performing the most
accurate impedance ratio measurements [3]. The
introduction of PSS allows to perform an automatic
bridge balance in a short time allowing to use the
bridge on a wide range of frequency and reducing
construction costs.
At CENAM, it is necessary to establish the
traceability chain between the ohm and the farad.
With the DAIB it will be possible to calibrate
individually two 100 kΩ resistors using as reference
standard a 10 kΩ Calculable Resistor constructed at
CENAM [4] at a frequency of 1592 Hz. These
resistors will be used in a Quadrature Bridge at 1592
Hz to calibrate two 1 nF standard capacitors [2].
Because the Calculable Resistor is calibrated with
traceability to the Quantum Hall Resistance (QHR)
then the capacitance calibration will be traced to the
QHR also.
2.
DESCRIPTION
OF
THE
ASSISTED IMPEDANCE BRIDGE
Fig. 1. Scheme of the Digitally Assisted Impedance
Bridge in a 10:1configuration.
DIGITALLY
The main difference between a Classic Impedance
Bridge and a DAIB is the use of PSS to introduce
1
Simposio de Metrología 2016
2.1.
19 al 23 de Septiembre de 2016
and a are the amplitude and phase of the voltage
signal Va.
Description of the Bridge
The voltage signal Va from the PSS give the
reference signal to the bridge and supply current to
the transformer Tp. The transformer TI is a two stage
IVD that generates the ratio of the bridge, and it is
powered directly by Tp. The high potential taps of the
resistance standards are connected to the ends taps
of TI, the high current taps are connected to Tp, the
low currents taps are connected together and the
low potential taps of the impedances are connected
to the ends taps of the Kelvin Inductive Divider Tk.
This divider together with the voltage signal Vd and
the injection transformer Td, provide the main
balance of the bridge and avoid the drop of potential
of the low current taps of the impedances. The four
pair impedance conditions [3] are achieved applying
voltage signals with Vb and Vc by means of the
injections transformers Tb and Tc, and measuring the
currents of the potential leads of the bridge through
the null detector and the detection transformers T2
and T3. The Wagner balance [3] is achieved by the
introductions of a voltage signal on the reference
ground node of the bridge by means of Vw and Tw
and measuring cero current in the reference node of
TI by the null detector. The main balance is
measured by the detection transformer T4 and the
null detector.
3.
With the DAIB is expected the calibration of 100 k
resistors at a frequency of 1592 Hz with an
uncertainty lower than 50 n/. This uncertainty can
be achieve thanks to the performance of TI [1];
however, the use of this kind of passive
electromagnetic devices limits the frequency scope
of the bridge in the 10:1 ratio measurements
because the 10:1 error of TI depends on the
frequency. So, the calibration of TI at 1592 Hz has
to be done in order to establish the ohm-farad
traceability chain. The Classic IVD Calibration
Systems requires expensive complex networks of
electromagnetic devices and an experienced
metrologist to perform the long time measurements,
at only one frequency. For this reason, it has been
considered to develop a Digitally Assisted IVD
Calibration System using the PSS. This may allow
performing the IVD calibration automatically and at
many frequencies in the audio range.
4.
REFERENCES
[1] G A. Kyriazis, J. A Moreno, J Melcher, “A TwoStage, Guarded Inductive Voltage Divider with
Small Ratio Errors for Coaxial Bridge
Applications“, ACTA IMEKO, December 2011,
issue 0, 5 – 9.
[2] L Callegaro, V D’Elia and B Trinchera,
“Realization of the farad from the dc quantum
Hall effect with digitally assisted impedance
bridges,”Metrologia 47, pp. 464-472, 2010
[3] B P Kibble, and G. H. Rayner, “Coaxial AC
Bridge”, (Bristol: Adam Hilger), 1984
[4] A H Pacheco, J A Moreno and F L HernandezMarquez, “Development of Calculable Resistors
at CENAM”, CPEM 2016 Digest, to be published.
Model of the Bridge
The model that describes the impedance ratio of the
bridge is in function of the type of impedances to be
measured. For now, the bridge aims to measure
resistance ratios. Equation 1 expresses the
calibration value of resistance Rx when the bridge is
on balance.
RX =RS
D
1
1-D 1+ RS (nAd cos (θd -θa ))
CONCLUSIONS
The design of a DAIB, the model for a resistance
calibration, advantages and disadvantages of the
bridge have been exposed. This bridge will be used
to calibrate a 100 k resistor at a frequency of 1592
Hz in order to get the ohm-farad traceability chain.
At this point, it can be seen that for each balance
measure node, there is one voltage signal that
balances the node: Vd for n4, Vb for n2, Vc for n3 and
Vw for n1. Each of these balances is performed
though a PC program adjusting the amplitude and
phase of the PSS signals in function of the null
detector measurements.
2.2.
DISCUTION AND FUTURE WORK
(1)
1-D Aa
where Rs is the value of the reference standard, D is
the complex ratio of TI, n is the number of windings
of the injection transformer Tb, Ad and d are the
amplitude and phase of the voltage signal Vd, and Aa
2